#GLF 1.0
#D Patterns whose population grows logarithmically have
#D long been known, but this is believed to be the first pattern
#D whose *diameter* grows logarithmically. It is based on a
#D blinker puffer that can be deleted by its own output (a blinker),
#D or push a block out by 8 cells.
#D
#D By Jason Summers with Gabriel Nivasch, 16 Aug 03
#D
#D Analysis by Dean Hickerson:
#D
#D Let g(n) be the generation in which the leading puffer is in the same
#D position as in gen 0, the block is 8n units to the right of its initial
#D position, and there are no blinkers in between.  I.e. the puffer is on its
#D way to push the block from position n to position n+1.  g(n) is always a
#D multiple of 240; the first few values are:
#D n   0   1   2    3    4    5    6    7     8     9    10    11    12
#D g(n)   0 240 720 1440 2400 3840 6000 9120 13680 20400 30240 44640 65760
#D g(n)/240   0   1   3    6   10   16   25   38    57    85   126   186   274
#D
#D Letting h(n)=g(n)/240, we have the recurrence
#D h(n) = h(n-1) + h(n-3) + 3.
#D
#D Also,
#D h(n) = round(C * R^n) - 3,
#D
#D where
#D R = (2 + cbrt(116 + 12 sqrt(93)) + cbrt(116 - 12 sqrt(93))) / 6
#D ~ 1.46557123187676802665673122521993910802557756847228570164318
#D
#D and
#D C = 1 + cbrt((13113 + 151 sqrt(93))/17298) +
#D cbrt((13113 - 151 sqrt(93))/17298)
#D ~ 2.82110012372929333835936935875070702572316547898891137253679
#D (C satisfies  31 C^3 - 93 C^2 + 16C - 1 = 0.)
#D
#D Since the diameter in generation g(n) is  8n + O(1),  we find that the
#D diameter in gen t is asymptotic to  A * log(t),  where
#D A = 8/log(R)
#D ~ 20.9289806366481084472899906014170877523092496362553746640196
x = -539, y = -83, width = 1077, height = 165
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13boo4b3o$214bo5bo6boo357boboo4b4o5boo8boo37boo3bo5bo10boo6b5o93bo13b
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109bo4bo20bobo14boo21boo10bobobbobo56bo6bobo6bobo46bo10bo17bobo78bo17b
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$213bobbobbo4b3o6boo121boo12bo5bo106bo4bo27bo7bobo5bobo26bobobbobo62b
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13b5o6boo22bobbo4bobbo11boo12boo219bo7boo15bo4bo10bo263bo63b3obb6obb3o
8bo$50boo5bo5boo132b3o10boo3boo51boo11bobbo220bo6boo16bo14bo164b3o95b
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125bobo69bo8bo6bo5bo$38bobo5boboo9boobbobo205bo9bobbo7bo52bob4obo10boo
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11bobo106bo110boo60b8o28bo309boo6boo11b3o3bobo4bobo172bo9bobbo7bo$20b
oo3boo11bobo9boo12bo106b3o207bobo336bo5b3o67bo115boo153boo6boo$20boo
15bobo130booboo207bobo342b3o6boo56bobo270bo7bo$37bo9bo121b3ob3o206bobb
o3boo335b3o7boo57boo268bobo5bobo$48boo11booboboo101b3ob3o191boo13bobo
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oo63bo$38b4o14b3o113bo105bo$19bobo15b6o10boob3o217b3o255bo$18b5o13b8o
9boobboo474bo532boo$17boo3boo11boo6boo7bo204b3o117b3o117b3o33b3o81b3o
117b3o16boo99b3o16boo99b3o16boo68boo$17boo3boo12b8o8boboo17bo182b5o
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181b3oboo114b3oboo114b3oboo18bo95b3oboo16b3o95b3oboo13booboo7bobbo85b
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10boo8boo93bo119bo36boo81bo29b3oboo84bo29b3oboo84bo29b3oboo4boo78bo29b
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76bo3bo32boo81bo3bo32boo81bo3bo32boo81bo3bo32boo81bo3bo32boo81bo3bo32b
oo$14bo97b4o116b4o36bo79b4o116b4o116b4o116b4o116b4o116b4o$123b4o116b4o
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148bo11boo$16b3o19bo6bo15bo112bobo446bo10boo5boo156bo19bo6boo147boo11b
oo$39b6o16bo111bobo446bobo10bobbo4bo165bo9bo133bo5boo13boo4boo$30bo30b
o75b8o28bo274boo10bo138boo3bobbo3boo11bo11bobo170bo5bobbo132bo3bo3b3o
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121bo105b4o65boo3boo3bo13bobo38bobo7boo6bo3boo88bobo74boo7bobo5bo56bo
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152boo7bo3bo7boo4b4o62boo29b3obobbobboo66bobo12b3o4bobb4o27bobbo8boo6b
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32boobbobboo8boo4boo57bo33bo14bo3bo90bo7bo16b4o59bo8bo10boo16bo81boo9b
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56bobo32boo12bo5bo88bo8bo3bo6boo5b4o58bo8bo9bobo77bo5bo41bobboboobobbo
166bobbo4bobbo4boo10boo5boo7bobo5bo20boo4bobbo4bobbo46b5o47bobbo4bobbo
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o19bobo8bobo12bo5bo66bobobbobo25bobo6bobo7bo23bobboo4boobbo21bo8bo11bo
155bo78boo66b6obb6o3boo10boo16bo26boo4bobbo4bobbo46booboo46b6obb6o15b
oo16bo20bo11bobbo4bobbo103bo3bo8b3o$21boo5b3o10bo4bobo64booboo3boo13bo
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76boo4bo62bobbo4bobbo5bo11bobo14boo31bobbo4bobbo18boo9boo15booboo47bo
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237boo6boo6b5oboo57boo6boo7boo10bo49boo6boo19bobo7bobo16b3o49boo6boo7b
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3o37bo47boo23bo132boo10bo5bo64boo5b3o5bobboo4bo72bobo40bo39boobboo6bo
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o106b5o80boo49bo10booboboo75boo4bo7bo8boo71boo3boo25b3o42boo6bo13boobo
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92b3o11bobobobo70boo8bo7bobboboobobbo123boo12bo81boo3boo41boo32bobo14b
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bo116boo14boo69bobo25boo3boo11bo50bobo9boo78bobo25boo3boo11bo60bobbo5b
oo48boo6b3o3b3o$99bo18b3o170b5o14boo36bobo91boo40boo7b3o4boo4bo163boo
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bb3o16b3o52b4o98bo3bo5bobb3o16b3o52b4o47b4o68boo3boo$98bobo5bobo124bo
bbo3boo49bo3bo14bo10b3o12boo10booboo6bobbo11bobo54boo5b3o52b3o4b3obo3b
o9boo142boo3bo5bo9bo3bo43bo13bobo6boboboo9boo80boo3bo5bo9bo3bo43bo13bo
bo6boboboo9boo35bo71boo3boo$106bo117boo6boo5b3oboobboo43b3o11bo11boboo
9boo15boobo6boo10boobbobo54boo6boo12boo39bobo4boobo3bo9boo142boobboobo
3bo8bo4bobo40bobo12bo3bo3bobbob3o8boo80boobboobo3bo8bo4bobo40bobo12bo
3bo3bobbob3o8boo$224boo4boo3bo3bo3bo3bobo43bo12boo10bobbo4bo5bo15bobo
5boo3bo8boo3bo66boo9boo40boo6boo3bo158bo5bo16boo4boo31boo4boo12bo4bobo
boo96bo5bo16boo4boo31boo4boo12bo4boboboo$116boo3boo109boo5bobo8bo7boo
37boobboo4boo9boboo5bo21bo8boo5boo7boo66boo61bobo14boo144bo3bo17boo4b
oo31boo4boo8bo4bo4b4o98bo3bo17boo4boo31boo4boo8bo4bo4b4o122bo$117b5o
111bobbobboo6bobbo7boo37boobboo4b3o11b3o3bo3bo27bobbo4bo6boo130bo15boo
146boo18boo37b3o17bo7bo101boo18boo37b3o17bo7bo122bobo$118b3o113bobo13b
o50boo4boo13boo5bo30bobo11boo311bobo10boo28bobo12bo3bo126bobo10boo28bo
bo12bo3bo132boo$119bo127bobo12boo29boo11boo379bo12boo29boo12bobo128bo
12boo29boo12bobo134boo$105bo7b3o131boo13boo29boo11bo724boo37b3o$104bob
o6bo917b3o35bobo$114bo907boo9boobo32boo$1022bo5bo4bobbo27bo$104b3o920b
o5boobo5b3o18boo$104b3o916bo3bo3b3o8b3o17boo4boobboo$105bo888bo30bo5b
oo8bo3bo15b3o4boobboo$995boo65boo4boo$116b3o875boo44boo3boo16boo$105bo
958bo$104b3o9bobo888bo$104b3o8b5o884b4o$114boo3boo313boo553b3o11b4o9b
oo$114boo3boo312boo556bo11bobbo9boo$104bobo321bo6bo6boo546bo12b4o5bo
37b5o$105bo322boo12bobo552boo5b4o4bo36bob3obo$117bo301boobboo4boo11bo
553bobo8bo42bo3bo$118boo299boobboo4b3o564bo54b3o$423boo4boo564boo45boo
8bo$120bo307boo8boo602boo$428bo9bobo$116bobbo320bo557boo$116boo322boo
543bo11bo3bo49boo$984bobo9bo5bo3boo43boo$984boo10bo3boboobboo$996bo5bo
$439bo522bo6bo27bo3bo$439bobo8bo510boo6boo10boo15boo$428boo12boo6bo
509b3o6b3o10boo$428boo12boo6bo510boo6boo10bo$442boo518bo6bo$439bobo$
439bo27bo4bo516b3o$445bo19boob4oboo513bo3bo$444bobo20bo4bo501bo$443bo
3bo526boo11bo5bo$443b5o525bobo11boo3boo$442boo3boo9boo504bo$443b5o9boo
504bobo$444b3o12bo491boo9bo3boo8bo13bo$445bo505boo9bo3boo5b4o12bobo$
962bo3boo4b4o9boobbobo$473bo489bobo6bobbo9boo4bo$466boobo3b4o487bo7b4o
5bo9bo$460boobboobobo4b4o5boo488b4o4bo6bobbo$459bobobbooboboo3bobbo5b
oo491bo12boo$449boo7b3o8boo3b4o$449boo6b3o8boo3b4o$458b3o12bo$445boo
12bobo$445boo13boo!
